非线性动力学和统计理论在地球物理流动中的应用 英文版PDF|Epub|txt|kindle电子书版本网盘下载

非线性动力学和统计理论在地球物理流动中的应用 英文版PDF格式电子书版下载

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1 Barotropic geophysical flows and two-dimensional fluid flows:elementary introduction1

1.1 Introduction1

1.2 Some special exact solutions8

1.3 Conserved quantities33

1.4 Barotropic geophysical flows in a channel domain-an important physical model44

1.5 Variational derivatives and an optimization principle for elementary geophysical solutions50

1.6 More equations for geophysical flows52

References58

2 The response to large-scale forcing59

2.1 Introduction59

2.2 Non-linear stability with Kolmogorov forcing62

2.3 Stability of flows with generalized Kolmogorov forcing76

References79

3 The selective decay principle for basic geophysical flows80

3.1 Introduction80

3.2 Selective decay states and their invariance82

3.3 Mathematical formulation of the selective decay principle84

3.4 Energy-enstrophy decay86

3.5 Bounds on the Dirichlet quotient,∧(t)88

3.6 Rigorous theory for selective decay90

3.7 Numerical experiments demonstrating facets of selective decay95

References102

A.1 Stronger controls on ∧(t)103

A.2 The proof of the mathematical form of the selective decay principle in the presence of the beta-plane effect107

4 Non-linear stability of steady geophysical flows115

4.1 Introduction115

4.2 Stability of simple steady states116

4.3 Stability for more general steady states124

4.4 Non-1inear stability of zonal flows on the beta-plane129

4.5 Variational characterization of the steady states133

References137

5 Topographic mean flow interaction,non-linear instability,and chaotic dynamics138

5.1 Introduction138

5.2 Systems with layered topography141

5.3 Integrable behavior145

5.4 A limit regime with chaotic solutions154

5.5 Numerical experiments167

References178

Appendix 1180

Appendix 2181

6 Introduction to information theory and empirical statistical theory183

6.1 Introduction183

6.2 Information theory and Shannon's entropy184

6.3 Most probable states with prior distribution190

6.4 Entropy for continuous measures on the line194

6.5 Maximum entropy principle for continuous fields201

6.6 An application of the maximum entropy principle to geophysical flows with topography204

6.7 Application of the maximum entropy principle to geophysical flows with topography and mean flow211

References218

7 Equilibrium statistical mechanics for systems of ordinary differential equations219

7.1 Introduction219

7.2 Introduction to statistical mechanics for ODEs221

7.3 Statistical mechanics for the truncated Burgers-Hopf equations229

7.4 The Lorenz 96 model239

References255

8 Statistical mechanics for the truncated quasi-geostrophic equations256

8.1 Introduction256

8.2 The finite-dimensional truncated quasi-geostrophic equations258

8.3 The statistical predictions for the truncated systems262

8.4 Numerical evidence supporting the statistical prediction264

8.5 The pseudo-energy and equilibrium statistical mechanics for fluctuations about the mean267

8.6 The continuum limit270

8.7 The role of statistically relevant and irrelevant conserved quantities285

References285

Appendix 1286

9 Empirical statistical theories for most probable states289

9.1 Introduction289

9.2 Empirical statistical theories with a few constraints291

9.3 The mean field statistical theory for point vortices299

9.4 Empirical statistical theories with infinitely many constraints309

9.5 Non-1inear stability for the most probable mean fields313

References316

10 Assessing the potential applicability of equilibrium statistical theories for geophysical flows:an overview317

10.1 Introduction317

10.2 Basic issues regarding equilibrium statistical theories for geophysical flows318

10.3 The central role of equilibrium statistical theories with a judicious prior distribution and a few external constraints320

10.4 The role of forcing and dissipation322

10.5 Is there a complete statistical mechanics theory for ESTMC and ESTP?324

References326

11 Predictions and comparison of equilibrium statistical theories328

11.1 Introduction328

11.2 Predictions of the statistical theory with a iudicious prior and a few external constraints for beta-plane channel flow330

11.3 Statistical sharpness of statistical theories with few constraints346

11.4 The limit of many-constraint theory(ESTMC)with small amplitude potential vorticity355

References360

12 Equilibrium statistical theories and dynamical modeling of flows with forcing and dissipation361

12.1 Introduction361

12.2 Meta-stability of equilibrium statistical structures with dissipation and small-scale forcing362

12.3 Crude closure for two-dimensional flows385

12.4 Remarks on the mathematical iustifications of crude closure405

References410

13 Predicting the jets and spots on Jupiter by equilibrium statistical mechanics411

13.1 Introduction411

13.2 The quasi-geostrophic model for interpreting observations and predictions for the weather layer of Jupiter417

13.3 The ESTP with physically motivated prior distribution419

13.4 Equilibrium statistical predictions for the jets and spots on Jupiter423

References426

14 The statistical relevance of additional conserved quantities for truncated geophysical flows427

14.1 Introduction427

14.2 A numerical 1aboratory for the role of higher-order invariants430

14.3 Comparison with equilibrium statistical predictions with a iudicious prior438

14.4 Statistically relevant conserved quantities for the truncated Burgers-Hopf equation440

References442

A.1 Spectral truncations of quasi-geostrophic flow with additional conserved quantities442

15 A mathematical framework for quantifying predictability utilizing relative entropy452

15.1 Ensemble prediction and relative entropy as a measure of predictability452

15.2 Quantifying predictability for a Gaussian prior distribution459

15.3 Non-Gaussian ensemble predictions in the Lorenz 96 model466

15.4 Information content beyond the climatology in ensemble predictions for the truncated Burgers-Hopf model472

15.5 Further developments in ensemble predictions and information theory478

References480

16 Barotropic quasi-geostrophic equations on the sphere482

16.1 Introduction482

16.2 Exact solutions,conserved quantities,and non-linear stability490

16.3 The response to large-scale forcing510

16.4 Selective decay on the sphere516

16.5 Energy enstrophy statistical theory on the unit sphere524

16.6 Statistical theories with a few constraints and statistical theories with many constraints on the unit sphere536

References542

Appendix 1542

Appendix 2546

Index550